This paper proposes an innovative two-stage data-driven optimization framework for a multi-energy system. Enormous energy conversion technologies are incorporated in the system to enhance the overall energy utilization efficiency, i.e., combined heat and power, power-to-gas, gas furnace, and ground source heat pump. Furthermore, a demand response program is adopted for stimulating the load shift of customers. Accordingly, both the economic performance and system reliability can be improved. The endogenous solar generation brings about high uncertainty and variability, which affects the decision making of the system operator. Therefore, a two-stage data-driven distributionally robust optimization (TSDRO) method is utilized to capture the uncertainty. A tractable semidefinite programming reformulation is obtained based on the duality theory. Case studies are implemented to demonstrate the effectiveness of applying the TSDRO on energy management.